The vehicle was purchased used and had similar symptoms at the time. It now has 137,000 miles on it. After getting alignments and replacing the tires, it is not as bad, but I might just have gotten more used to it. Since it has been through a few sets of tires now, it has eliminated my suspicion of the wheels being out of balance.

Did you noticed unusual tires wear? This may be a sign that its still unaligned. I've a the same issue with my car and it took 2 different garage to solve the issue.
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Gabriel MongeonMay 5 '11 at 13:49

@jzd - Does the vibration happen while simply maintaining those speeds, or is it as you accelerate through them?
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IsziMay 9 '11 at 4:56

The vast majority of vibrations that come and go at various speeds are wheel and/or driveshaft balance issues. They come and go due to exciting the suspension/steering when reaching resonant frequencies. Yours may be a wheel issue that shops would rather balance as well as they can than tell you you should replace a wheel.

There are more expensive ways to get your tires balanced, if it merits it. Some shops can provide road force balancing that takes into consideration the tires deflection when in contact with road surface for balancing.

However, first I would take the car back to the last tire shop and ask them to re-balance it more precisely. "Lifetime" balance deals are popular for major repair chains. Perhaps asking for "sticky" weights that go on the inside middle of the wheel as something different to try.